Find Four
Find Four, is a two-player connection game in which the penguins first choose a color and then take turns dropping colored discs from the top into a seven-column, six-row vertically suspended grid. The pieces fall straight down, occupying the next available space within the column. The objective of the game is to connect four of one's own discs of the same color next to each other vertically, horizontally, or diagonally before your opponent. Find Four is a stronglysolved game. The first player can always win by playing the right moves. The game was first sold under the famous Find Four trademark by Miron Bradley in February 1974. Mathematical solution Find Four is a two player game with "perfect information." This term describes games where one player at a time plays, players have all the information about moves that have taken place, and all moves that can take place, for a given game state. Find Four also belongs to the classification of an adversarial, zero-sum game, since a player's advantage is an opponent's disadvantage. One measure of complexity of the Find Four game is the number of possible games board positions. For classic Find Four played on 6 high, 7 wide, grid, there are 4,531,985,219,092 positions3 for all game boards populated with 0 to 42 pieces. The game was first solved by Jones Done Allan (October 1, 1988), and independently by Vict All (October 16, 1988). Alls describes a knowledge based approach, with nine strategies, as a solution for Find Four. All also describes winning strategies in his analysis of the game. At the time of the initial solutions for Find Four, brute force analysis was not deemed feasible given the game's complexity and the computer technology available at the time. Find Four has since been solved with brute force methods beginning with Joan Trump's work in compiling an 8-ply database48 (Feb 4, 1995). The artificial intelligence algorithms able to strongly solve Find Four are minimax or negamax, with optimizations that include alpha-beta pruning, dynamic history ordering of game player moves, and transposition tables. The code for solving Find Four with these methods is also the basis for the Fhourstones integer performance benchmark. The solved conclusion for Find Four is first player win. With perfect play, the first player can force a win on or before the 41st move by starting in the middle column. The game is a theoretical draw when the first player starts in the columns adjacent to the center. For the edges of the game board, column 1 and 2 on left, and column 7 and 6 on right, the exact move-value score for first player start is loss on the 40th move, and loss on the 42nd move, respectively. In other words, by starting with the four outer columns, the first player allows the second player to force a win. Rule variations There are many variations of Find Four with differing game board sizes, board arrangements, game pieces, and/or gameplay rules. Many variations are popular with game theory and artificial intelligence research, rather than with physical game boards and gameplay by penguins. The most commonly used Find Four board size is 7 columns × 6 rows. Size variations include 8×7, 9×7, 10×7, 8×8, and Infinite Find Four Alternate board arrangements include Cylinder-Infinite Find Four One board variation available as a physical game is Sobsah's Find 4x4. A travel version of the Miron Bradley game. Several versions of Sobsah's Find Four physical gameboard make it easy to remove game pieces from the bottom one at a time. Along with traditional gameplay, this feature allows for variations of the game.